The mass density function of a substance is given by: p(x,y) = (x^2+y^2)*e^(-x^2-y^2). A particle is moving along the hyperbola x^2-y^2=1 with the parametric function h(t)=(cosh(t),sinh(t)) for t in (-1,1). a) Determine the time t when the density of the particle is maximized. b) Find the tangent vector to the path of the particle at the time t determined in part (a). c) Calculate the rate of change of the density of the particle at the time t obtained in part (a)